Is This Correct? Let’s Check!

Authors Omri Ben-Eliezer , Dan Mikulincer , Elchanan Mossel , Madhu Sudan

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Omri Ben-Eliezer
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Dan Mikulincer
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Elchanan Mossel
  • Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
Madhu Sudan
  • School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

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Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel, and Madhu Sudan. Is This Correct? Let’s Check!. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 15:1-15:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


Societal accumulation of knowledge is a complex process. The correctness of new units of knowledge depends not only on the correctness of new reasoning, but also on the correctness of old units that the new one builds on. The errors in such accumulation processes are often remedied by error correction and detection heuristics. Motivating examples include the scientific process based on scientific publications, and software development based on libraries of code. Natural processes that aim to keep errors under control, such as peer review in scientific publications, and testing and debugging in software development, would typically check existing pieces of knowledge - both for the reasoning that generated them and the previous facts they rely on. In this work, we present a simple process that models such accumulation of knowledge and study the persistence (or lack thereof) of errors. We consider a simple probabilistic model for the generation of new units of knowledge based on the preferential attachment growth model, which additionally allows for errors. Furthermore, the process includes checks aimed at catching these errors. We investigate when effects of errors persist forever in the system (with positive probability) and when they get rooted out completely by the checking process. The two basic parameters associated with the checking process are the probability of conducting a check and the depth of the check. We show that errors are rooted out if checks are sufficiently frequent and sufficiently deep. In contrast, shallow or infrequent checks are insufficient to root out errors.

Subject Classification

ACM Subject Classification
  • Networks → Error detection and error correction
  • Error Propagation
  • Preferential Attachment


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